Representation stability for homotopy automorphisms
Algebraic Topology
2024-08-28 v3
Abstract
We consider in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces and boundary relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated FI-modules, and thus satisfy representation stability for symmetric groups, in the sense of Church and Farb.
Cite
@article{arxiv.2105.11325,
title = {Representation stability for homotopy automorphisms},
author = {Erik Lindell and Bashar Saleh},
journal= {arXiv preprint arXiv:2105.11325},
year = {2024}
}
Comments
Version 2. Major revision. Explicit stability ranges added to Theorem A and Theorem B. Proof added that the FI-Q-module considered in Theorem B is the rationalization of an FI-Z-module, constructed in a geometric way. Accepted for publication in "Algebraic and Geometric Topology"